Math Problem Statement

Find an equation for the line in the given graph.

Solution

The graph in the image shows a line with a negative slope crossing the y-axis and x-axis at specific points. To find the equation of the line, we can use the slope-intercept form of a linear equation, which is:

y=mx+by = mx + b

Where:

  • mm is the slope of the line.
  • bb is the y-intercept (the point where the line crosses the y-axis).

Step 1: Identify two points on the line.

From the graph, two clear points on the line are:

  • (0,6)(0, 6), which is the y-intercept.
  • (4,0)(4, 0), which is the x-intercept.

Step 2: Calculate the slope mm.

The formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Substitute the points (0,6)(0, 6) and (4,0)(4, 0):

m=0640=64=32m = \frac{0 - 6}{4 - 0} = \frac{-6}{4} = -\frac{3}{2}

Step 3: Write the equation.

Now that we have the slope m=32m = -\frac{3}{2} and the y-intercept b=6b = 6, the equation of the line is:

y=32x+6y = -\frac{3}{2}x + 6

This is the equation of the line in slope-intercept form.

Let me know if you'd like further details or have any questions!

Related Questions:

  1. How do you find the slope from a graph if no clear points are given?
  2. What is the point-slope form of a line equation, and how does it relate to the slope-intercept form?
  3. How do you convert the equation from slope-intercept form to standard form?
  4. What does the slope tell us about the direction of the line?
  5. How can you verify if a point lies on a line given its equation?

Tip: Always check your points carefully when calculating the slope, especially for signs (positive or negative).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Slope-Intercept Form

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b

Theorems

Slope-Intercept Form Theorem

Suitable Grade Level

Grades 8-10